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An a.c. generator is connected to a seal...

An a.c. generator is connected to a sealed box through a pair of terminals. The box may cantain R,L,C or series combination of any two of the three elements. Measurements made outside the box show that `E = (75 sin omega t)` volt and `I = 1.2 sin (omega t + pi//5) A`
(i) Name the circuit elements
(ii) What is the power factor of the circuit
(iii) What is the rat at which energy is delivered by the generator to the circuit ?

Text Solution

Verified by Experts

Here, `E = (75 sin omega t)` volt and
`I = 1.2 sin (omega t + pi//5)`
As current leads the e.m.f by a phase angle `pi//5`, therefore, the box must contain a series combination of resistor (R ) and capacitor (C ).
(ii) Power factor of the circuit is
`cos phi = cos pi//5 = 0.81`
(iii) Rate at which energy is delivered by the generator to the circuit is
`P = E_(v) I_(v) cos phi`
`P = (75)/(sqrt2)xx(1.2)/(sqrt2)xx0.81 = 36.45` watt
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